Curved mesh topology 2
"but I want curved edges after applying the modifier"
There is no such thing as curved edges, edges are by definition strictly straight.

If you zoom in on one those apparently "curved" edges you will find that they are still in fact straight, just like before, just subdivided more finely into smaller straight segments.

And that is the basis of Subdivision Modelling you use a Subdivision Surface modifier to give the impression of curvature adjusted to a desired level of detail, but there never really is any true absolute curvature. There is always a fine balance between desired level detail and capable performance.

Anyway if you mean to say that you want to see the result of the Subdivision Surface modifier while modifying your mesh in Edit Mode you can activate the option Adjust Edit Cage to Modifier Results in the modifier header. You should for the most part never apply your modifier, and work on a low poly, good topology base mesh, while letting Blender do the hard work of subdividing it dynamically and non destructively.



If you want "true curvature" you should be using a different type of modelling software with a geometry engine based on NURBS surfaces, where curvature is mathematically described, and surfaces controlled with control points.

And even then you would find that a computer is only really capable of displaying straight segments, and those apparently curved surfaces are still actually composed of straight segments, only they are dynamically generated and usually harder to spot to the naked eye.